{"title":"Quasi-Permutation Representations for the Group SL(2, q) when Extended by a Certain Group of Order Two","authors":"M. Ghorbany","volume":9,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":463,"pagesEnd":466,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9999254","abstract":"
A square matrix over the complex field with non- negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful representation of G by quasi-permutation matrices over the rationals and the complex numbers are denoted by q(G) and c(G) respectively. Finally r (G) denotes the minimal degree of a faithful rational valued complex character of C. The purpose of this paper is to calculate q(G), c(G) and r(G) for the group S L(2, q) when extended by a certain group of order two.<\/span><\/p>\r\n","references":"[1] H. Behravesh, \"Quasi-permutation representations of p-groups of class 2\", J. London Math. Soc. (2)55(1997) 251-26.\r\n[2] H. Behravesh, \"The rational character table of special linear groups\", J. Sci. I.R.I. Vol. 9 No. 2(1998) 173-180.\r\n[3] J. M. Burns, b. Goldsmith, B. Hartley and R. Sandling, \"on quasi-permutation representations of finite groups\", Glasgow Math, J. 36(1994) 301-308.\r\n[4] M. Darafsheh, F. Nowroozi Larki, \"Equivalance Classes of Matrices in GL(2,q) and SL(2,q) and related topics\", Korean J. Comput. Appl. Math. 6(1999), no.2,331-344.\r\n[5] L. Dornhoff, \"Group Representation Theory\", Part A, Marcel Dekker, New York, 1971.\r\n[6] W. Fiet, \"Extension of Cuspidal Characters of GL(m,q)\", Publications Mathematicae, 34(1987), 273-297.\r\n[7] J. A. Green, \"The Characters of the Finite General Linear Groups\", Trans. Amer. Math. Soc. 80 (1955) 405-447.\r\n[8] I.M. Isaacs, \"Character theory of finite groups\", Academic Press, Newyork, 1976.\r\n[9] M.A. Shahabi Shojaei, \"Schur indices of irreducible characters of SL(2,q)\", Arch. Math. 221-131, 1983.\r\n[10] W. J. Wong, Linear groups analogous to permutation groups, J. Austral. Math. Soc. (Sec. A) 3, 180-184, 1963.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 9, 2007"}